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ENDS 375

Foundations of Visualization

9/7/04 Notes

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Image Statistics

Useful input into computational algorithms

–measures of image quality

–basis for automated decisions about images

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Image Statistics

Arithmetic Meanmean = sum(Pxy)/(x*y)

Variance

variance = (sum(Pxy*Pxy)/(x*y)-mean*mean)

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Image Statistics

Standard Deviation

stdev = square root (variance) Histogram

– two axis plot of pixel values vs number of pixels

– basis for deciding - contrast range, overall brightness, thresholding, ...

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Point Operations on Images Numeric Transformations Transfer Functions Often implemented using look-up tables

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Specific Operations

(not usually reversible) Unity

Invert

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Specific Operations

Contrast Adjustment

Higher

Lower

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Specific Operations

Threshold

Gamma

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Color Modification

LessRed

MoreYellow

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Arithmetic Operations

Two or more images

Cxy = Axy < operation > Bxy

– Addition

– Subtraction

– Averaging, etc ...

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Logical Operations

and, or

nand, nor

xor, xnor

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Image Averaging

Add corresponding pixels from multiple images then divide by the number of images

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Alpha Blending

Cxy = Axy*Mxy

+ Bxy*(max -Mxy )

“Blends” two images

Need a “matte” imageBasis for image compositing

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Compositing

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Neighborhood Operations

Each output pixel depends on its neighbors in the original

Convolution - the basic operation Image Filters Sampling

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Convolution

Each pixel the sum ofneighborhoodand kernel

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Image Filters

low-pass filters

Box or Gaussian filters

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High-pass

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Edge detection

LaPlacian Filter

also Sobel and Prewitt

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Embossing

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Object Correlation

Pattern matching to find specific shapes in an image

Use shape specific kernels

Orientation sensitive

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Other Filters

Statistical

median, max, min Sharpening

unsharpening maskcombine two versions of the same image

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Degraining

Uses

“maxmin” or

“minmax “

filters

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Sampling

Creating a new image based on multi-pixel information from the original image

Sub-pixel information

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Sampling

Forward Transformation

from source to destination

Inverse Transformation

from destination to source

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Sampling

Nearest Neighbor

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Bilinear Interpolation

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Geometric Operations

Scaling Rotation Translation Operation ordering important

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Warping

Polynomial warping Morphing

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Morphological Operations

Usually on one-bit images–Erosion

–Dilation

–Hit-or-Miss

–Outlining

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“Pipelined” Operations

Sequences of operationsShrinking - center of “mass”

Thinning - equidistant from boundaries

Skeletonization - “burn” together

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Readings

Course notes section 1-7 Course notes section 1-8 Course notes section 1-9 Textbook - Chapter 14